ci.cv {MBESS}

Confidence interval for the coefficient of variation

Description

Function to calculate the confidence interval for the population coefficient of variation using the noncentral t-distribution.

Usage

ci.cv(cv=NULL, mean = NULL, sd = NULL, n = NULL, data = NULL, 
conf.level = 0.95, alpha.lower = NULL, alpha.upper = NULL, ...)

Arguments

cv

coefficient of variation

mean

sample mean

sd

sample standard deviation (square root of the unbiased estimate of the variance)

n

sample size

data

vector of data for which the confidence interval for the coefficient of variation is to be calculated

conf.level

desired confidence level (1-Type I error rate)

alpha.lower

the proportion of values beyond the lower limit of the confidence interval (cannot be used with conf.level).

alpha.upper

the proportion of values beyond the upper limit of the confidence interval (cannot be used with conf.level).

...

allows one to potentially include parameter values for inner functions

Details

Uses the noncentral t-distribution to calculate the confidence interval for the population coefficient of variation.

Value

Lower.Limit.CofV

Lower confidence interval limit

Prob.Less.Lower

Proportion of the distribution beyond Lower.Limit.CofV

Upper.Limit.CofV

Upper confidence interval limit

Prob.Greater.Upper

Proportion of the distribution beyond Upper.Limit.CofV

C.of.V

Observed coefficient of variation

Author(s)

Ken Kelley (University of Notre Dame; [e-mail])

References

Johnson, B. L., & Welch, B. L. (1940). Applications of the non-central t-distribution. Biometrika, 31, 362–389.

Kelley, K. (2007). Sample size planning for the coefficient of variation from the accuracy in parameter estimation approach. Behavior Research Methods, 39 (4), 755–766.

Kelley, K. (2007). Constructing confidence intervals for standardized effect sizes: Theory, application, and implementation. Journal of Statistical Software, 20 (8), 1–24.

McKay, A. T. (1932). Distribution of the coefficient of variation and the extended t distribution, Journal of the Royal Statistical Society, 95, 695–698.

See Also

cv

Examples

set.seed(113)
N <- 15
X <- rnorm(N, 5, 1)
mean.X <- mean(X)
sd.X <- var(X)^.5

ci.cv(mean=mean.X, sd=sd.X, n=N, alpha.lower=.025, alpha.upper=.025,
conf.level=NULL)
ci.cv(data=X, conf.level=.95)
ci.cv(cv=sd.X/mean.X, n=N, conf.level=.95)